Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem

Studies in Fuzziness and Soft Computing

Volumn 219, Issue , 2008, Pages 633-664

  Smets, Philippe ^a  

^a NONE

Author keywords

Baye's theorem; Belief functions; Disjunctive rule of combination

Indexed keywords

EID: 38649135395     PISSN: 14349922     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-44792-4_25     Document Type: Article

References (37)

1. Cohen, M.S., Laskey, K.B. and Ulvila, J.W. (1987) The management uncertainty in intelligence data: A self-reconciling evidential database. Falls Church, VA: Decision Science Consortium, Inc.
2. Delgado M. and Moral S. (1987) On the concept of possibility-probabilty consistency. Fuzzy Sets and Systems 21: 311-3018.
3. Dubois D. and Prade H. (1985) Théorie des possibilités. Masson, Paris.
4. Dubois D. and Prade H. (1986a) A set theoretical view of belief functions. Int. J. Gen. Systems, 12: 193-226.
5. Dubois D. and Prade H. (1986b) On the unicity of Dempster rule of combination. Int. J. Intelligent Systems, 1: 133-142.
6. Dubois D. and Prade H. (1987) The principle of minimum specificity as a basis for evidential reasoning. in: Uncertainty in knowledge-based systems, Bouchon B. and Yager R. eds, Springer Verlag, Berlin, p. 75-84.
7. Dubois D. and Prade H. (1988) Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence, 4: 244-264.
8. Edwards A.W.F. (1972) Likelihood. Cambridge University Press, Cambridge, UK.
9. Gebhardt F. and Kruse R. (1993) The context model: An integrating view vagueness and uncertainty. Int. J. Approx. Reas. 9(3), 283-314.
10. Hacking I. (1965) Logic of statistical inference. Cambridge University Press, Cambridge, U.K.
11. Halpern J.Y. and Fagin R. (1990) Two views of belief: Belief as Generalized Probability and Belief as Evidence. Proc. Eighth National Conf. on AI 112-119.
12. Hsia Y.-T. (1991) Characterizing Belief with Minimum Commitment. IJCAI-91: 1184-1189.
13. Kennes R. and Smets Ph. (1990) Computational Aspects of the Mšbius Transform. Procs of the 6th Conf. on Uncertainty in AI, Cambridge, USA.
14. Klawonn F. and Schwecke E. (1992) On the axiomatic justification of Dempster's rule of combination. Int. J. Intel. Systems 7: 469-478.
15. Klawonn F. and Smets Ph. (1992) The dynamic of belief in the transferable belief model and specialization-generalization matrices. in Dubois D., Wellman M.P., d'Ambrosio B. and Smets P. Uncertainty in AI 92. Morgan Kaufmann, San Mateo, Ca, USA, 1992, p. 130-137.
16. Kruse R. and Schwecke E. (1990) Specialization: A new concept for uncertainty handling with belief functions. Int. J. Gen. Systems 18: 49-60.
17. Kohlas J. and Monney P. A. (1990) Modeling and reasoning with hints. Technical Report. Inst. Automation and OR. Univ. Fribourg.
18. Moral S. (1985) Información difusa. Relationes entre probabilidad y possibilidad. Tesis Doctoral, Universidad de Granada.
19. Nguyen T. H. and Smets Ph. (1993) On Dynamics of Cautious Belief and Conditional Objects. Int. J. Approx. Reas. 8(2), 89-104.
20. Pearl J. (1988) Probabilistic reasoning in intelligent systems: Networks of plausible inference. Morgan Kaufmann Pub. San Mateo, Ca, USA.
21. Pearl J. (1990) Reasoning with Belief Functions: An Analysis of Compatibility. Intern. J. Approx. Reasoning, 4: 363-390.
22. Shafer G. (1976) A mathematical theory of evidence. Princeton Univ. Press. Princeton, NJ.
23. Shafer G. (1982) Belief functions and parametric models. J. Roy. Statist. Soc. B44 322-352.
24. Shafer G., Shenoy P.P. and Mellouli K. (1987) Propagating belief functions in qualitative Markov trees. Int. J. Approx. Reasoning, 1: 349-400.
25. Smets Ph. (1978) Un modèle mathématico-statistique simulant le processus du diagnostic médical. Doctoral dissertation, Université Libre de Bruxelles, Bruxelles, (Available through University Microfilm International, 30-32 Mortimer Street, London W1N 7RA, thesis 80-70, 003)
26. Smets Ph. (1981) Medical Diagnosis: Fuzzy Sets and Degrees of Belief. Fuzzy Sets and systems, 5: 259-266.
27. Smets P. (1982) Possibilistic Inference from Statistical Data. In: Second World Conference on Mathematics at the Service of Man. A. Ballester, D. Cardus and E. Trillas eds. Universidad Politecnica de Las Palmas, pp. 611-613.
28. Smets Ph. (1986) Bayes' theorem generalized for belief functions. Proc. ECAI-86, vol. II. 169-171, 1986.
29. Smets Ph. (1988) Belief functions. in Smets Ph, Mamdani A., Dubois D. and Prade H. ed. Non standard logics for automated reasoning. Academic Press, London p. 253-286.
30. Smets Ph. (1990) The combination of evidence in the transferable belief model. IEEE Trans. Pattern analysis and Machine Intelligence, 12: 447-458.
31. Smets Ph. (1991) The Transferable Belief Model and Other Interpretations of Dempster-Shafer's Model. in Bonissone P.P., Henrion M., Kanal L.N. and Lemmer J.F. eds. Uncertainty in Artificial Intelligence 6, North Holland, Amsterdam, 375-384.
32. Smets Ph. (1992a) Resolving misunderstandings about belief functions: A response to the many criticisms raised by J. Pearl. Int. J. Approximate Reasoning.6: 321-344.
33. Smets Ph. (1992b) The nature of the unnormalized beliefs encountered in the transferable belief model. in Dubois D., Wellman M.P., d'Ambrosio B. and Smets P. Uncertainty in AI 92. Morgan Kaufmann, San Mateo, Ca, USA, 1992, p. 292-297.
34. Smets Ph. (1992c) The concept of distinct evidence. IPMU 92 Proceedings, p. 789-794.
35. Smets P. and Kennes R. (1994) The transferable belief model. Artificial Intelligence, 66(2), 191-234.
36. Yager R. (1986) The entailment principle for Dempster-Shafer granules. Int. J. Intell. Systems 1: 247-262
37. Zadeh L.A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. 1: 3-28.